Recent progresses of quantum confinement in graphene quantum dots

Si-Yu Li, Lin He

PDF(4585 KB)
PDF(4585 KB)
Front. Phys. ›› 2022, Vol. 17 ›› Issue (3) : 33201. DOI: 10.1007/s11467-021-1125-2
TOPICAL REVIEW
TOPICAL REVIEW

Recent progresses of quantum confinement in graphene quantum dots

Author information +
History +

Abstract

Graphene quantum dots (GQDs) not only have potential applications on spin qubit, but also serve as essential platforms to study the fundamental properties of Dirac fermions, such as Klein tunneling and Berry phase. By now, the study of quantum confinement in GQDs still attract much attention in condensed matter physics. In this article, we review the experimental progresses on quantum confinement in GQDs mainly by using scanning tunneling microscopy (STM) and scanning tunneling spectroscopy (STS). Here, the GQDs are divided into Klein GQDs, bound-state GQDs and edge-terminated GQDs according to their different confinement strength. Based on the realization of quasi-bound states in Klein GQDs, external perpendicular magnetic field is utilized as a manipulation approach to trigger and control the novel properties by tuning Berry phase and electron–electron (e–e) interaction. The tip-induced edge-free GQDs can serve as an intuitive mean to explore the broken symmetry states at nanoscale and single-electron accuracy, which are expected to be used in studying physical properties of different two-dimensional materials. Moreover, high-spin magnetic ground states are successfully introduced in edge-terminated GQDs by designing and synthesizing triangulene zigzag nanographenes.

Graphical abstract

Keywords

graphene quantum dot / scanning tunneling microscopy / scanning tunneling spectroscopy / quasi-bound state / bound state / triangulene

Cite this article

Download citation ▾
Si-Yu Li, Lin He. Recent progresses of quantum confinement in graphene quantum dots. Front. Phys., 2022, 17(3): 33201 https://doi.org/10.1007/s11467-021-1125-2

References

[1]
D. Loss and D. P. DiVincenzo , Quantum computation with quantum dots, Phys. Rev. A 57 (1), 120 (1998)
CrossRef ADS Google scholar
[2]
J. Elzerman , R. Hanson , L. W. Van Beveren , B. Witkamp , L. Vandersypen , and L. P. Kouwenhoven , Single-shot read-out of an individual electron spin in a quantum dot, Nature 430, 431 (2004)
CrossRef ADS Google scholar
[3]
R. Hanson , L. W. van Beveren , I. Vink , J. Elzerman , W. Naber , F. Koppens , L. Kouwenhoven , and L. Vandersypen , Single-shot readout of electron spin states in a quantum dot using spin-dependent tunnel rates, Phys. Rev. Lett. 94 (19), 196802 (2005)
CrossRef ADS Google scholar
[4]
F. H. Koppens , C. Buizert , K. J. Tielrooij , I. T. Vink , K. C. Nowack , T. Meunier , L. Kouwenhoven , and L. Vandersypen , Driven coherent oscillations of a single electron spin in a quantum dot, Nature 442 (7104), 766 (2006)
CrossRef ADS Google scholar
[5]
J. R. Petta , A. C. Johnson , J. M. Taylor , E. A. Laird , A. Yacoby , M. D. Lukin , C. M. Marcus , M. P. Hanson , and A. C. Gossard , Coherent manipulation of coupled electron spins in semiconductor quantum dots, Science 309 (5744), 2180 (2005)
CrossRef ADS Google scholar
[6]
B. Trauzettel , D. V. Bulaev , D. Loss , and G. Burkard , Spin qubits in graphene quantum dots, Nat. Phys. 3 (3), 192 (2007)
CrossRef ADS Google scholar
[7]
J. Lee , D. Wong , J. F. Jr Velasco , S. Rodriguez-Nieva , H. Z. Kahn , T. Tsai , K. Taniguchi , A. Watanabe , Zettl , F. Wang , L. S. Levitov , and M. F. Crommie , Imaging electrostatically confined Dirac fermions in graphene quantum dots, Nat. Phys. 12 (11), 1032 (2016)
CrossRef ADS Google scholar
[8]
C. Gutiérrez , L. Brown , C. J. Kim , J. Park , and A. N. Pasupathy , Klein tunnelling and electron trapping in nanometre-scale graphene quantum dots, Nat. Phys. 12 (11), 1069 (2016)
CrossRef ADS Google scholar
[9]
P. G. Silvestrov and K. B. Efetov , Quantum dots in graphene, Phys. Rev. Lett. 98 (1), 016802 (2007)
CrossRef ADS Google scholar
[10]
K. K. Bai , J. J. Zhou , Y. C. Wei , J. B. Qiao , Y. W. Liu , H. W. Liu , H. Jiang , and L. He , Generating atomically sharp p–n junctions in graphene and testing quantum electron optics on the nanoscale, Phys. Rev. B 97 (4), 045413 (2018)
CrossRef ADS Google scholar
[11]
Y. Jiang , J. Mao , D. Moldovan , M. R. Masir , G. Li , K. Watanabe , T. Taniguchi , F. M. Peeters , and E. Y. Andrei , Tuning a circular p–n junction in graphene from quantum confinement to optical guiding, Nat. Nanotechnol. 12 (11), 1045 (2017)
CrossRef ADS Google scholar
[12]
F. Ghahari , D. Walkup , C. Gutiérrez , J. F. RodriguezNieva , Y. Zhao , J. Wyrick , F. D. Natterer , W. G. Cullen , K. Watanabe , T. Taniguchi , L. S. Levitov , N. B. Zhitenev , and J. A. Stroscio , An on/off Berry phase switch in circular graphene resonators, Science 356 (6340), 845 (2017)
CrossRef ADS Google scholar
[13]
Y. W. Liu , Z. Hou , S. Y. Li , Q. F. Sun , and L. He , Movable valley switch driven by Berry phase in bilayergraphene resonators, Phys. Rev. Lett. 124 (16), 166801 (2020)
CrossRef ADS Google scholar
[14]
Z. Q. Fu , K. K. Bai , Y. N. Ren , J. J. Zhou , and L. He , Coulomb interaction in quasibound states of graphene quantum dots, Phys. Rev. B 101 (23), 235310 (2020)
CrossRef ADS Google scholar
[15]
Y. Zhao , J. Wyrick , F. D. Natterer , J. F. RodriguezNieva , C. Lewandowski , K. Watanabe , T. Taniguchi , L. S. Levitov , N. B. Zhitenev , and J. A. Stroscio , Creating and probing electron whispering-gallery modes in graphene, Science 348 (6235), 672 (2015)
CrossRef ADS Google scholar
[16]
N. M. Freitag , L. A. Chizhova , P. Nemes-Incze , C. R. Woods , R. V. Gorbachev , Y. Cao , A. K. Geim , K. S. Novoselov , J. Burgdorfer , F. Libisch , and M. Morgenstern , Electrostatically confined monolayer graphene quantum dots with orbital and valley splittings, Nano Lett. 16 (9), 5798 (2016)
CrossRef ADS Google scholar
[17]
S. Y. Li , Y. Su , Y. N. Ren , and L. He , Valley polarization and inversion in strained Graphene via pseudo-Landau levels, valley splitting of real Landau levels, and confined states, Phys. Rev. Lett. 124 (10), 106802 (2020)
CrossRef ADS Google scholar
[18]
L. A. Ponomarenko , F. Schedin , M. I. Katsnelson , R. Yang , E. W. Hill , K. S. Novoselov , and A. K. Geim , Chaotic Dirac billiard in graphene quantum dots, Science 320 (5874), 356 (2008)
CrossRef ADS Google scholar
[19]
S. Mishra , D. Beyer , K. Eimre , J. Liu , R. Berger , O. Gröning , C. A. Pignedoli , K. Müllen , R. Fasel , X. Feng , and P. Ruffeux , Synthesis and characterization of π-extended triangulene, J. Am. Chem. Soc. 141 (27), 10621 (2019)
CrossRef ADS Google scholar
[20]
S. Mishra , D. Beyer , K. Eimre , R. Ortiz , J. Fernández‐Rossier , R. Berger , O. Gröning , C. A. Pignedoli , R. Fasel , X. Feng , and P. Ruffeux , Collective all‐carbon magnetism in triangulene dimers, Angew. Chem. Int. Ed. 59 (29), 12041 (2020)
CrossRef ADS Google scholar
[21]
J. Su , M. Telychko , P. Hu , G. Macam , P. Mutombo , H. Zhang , Y. Bao , F. Cheng , Z. Q. Huang , Z. Qiu , S. J. R. Tan , H. Lin , P. Jelínek , F. C. Chuang , J. Wu , and J. Lu , Atomically precise bottom-up synthesis of π-extended [5]triangulene, Sci. Adv. 5 (7), eaav7717 (2019)
CrossRef ADS Google scholar
[22]
N. M. Freitag , T. Reisch , L. A. Chizhova , P. Nemes-Incze , C. Holl , C. R. Woods , R. V. Gorbachev , Y. Cao , A. K. Geim , K. S. Novoselov , J. Burgdörfer , F. Libisch , and M. Morgenstern , Large tunable valley splitting in edge-free graphene quantum dots on boron nitride, Nat. Nanotechnol. 13 (5), 392 (2018)
CrossRef ADS Google scholar
[23]
S.-Y. Li , Y.-N. Ren , Y.-W. Liu , M.-X. Chen , H. Jiang , and L. He , Nanoscale detection of valley-dependent spin splitting around atomic defects of graphene, 2D Mater. 6, 031005 (2019)
CrossRef ADS Google scholar
[24]
S. Jung , G. M. Rutter , N. N. Klimov , D. B. Newell , I. Calizo , A. R. Hight-Walker , N. B. Zhitenev , and J. A. Stroscio , Evolution of microscopic localization in graphene in a magnetic field from scattering resonances to quantum dots, Nat. Phys. 7 (3), 245 (2011)
CrossRef ADS Google scholar
[25]
A. H. Castro Neto , F. Guinea , N. M. R. Peres , K. S. Novoselov , and A. K. Geim , The electronic properties of graphene, Rev. Mod. Phys. 81 (1), 109 (2009)
CrossRef ADS Google scholar
[26]
M. Katsnelson , K. Novoselov , and A. Geim , Chiral tunnelling and the Klein paradox in graphene, Nat. Phys. 2 (9), 620 (2006)
CrossRef ADS Google scholar
[27]
V. Pereira , F. Mlinar , F. M. Peeters , and P. Vasilopoulos , Confined states and direction-dependent transmission in graphene quantum wells, Phys. Rev. B 74 (4), 045424 (2006)
CrossRef ADS Google scholar
[28]
M. Barbier , F. Peeters , P. Vasilopoulos , and Pereira , Dirac and Klein-Gordon particles in one-dimensional periodic potentials, Phys. Rev. B 77 (11), 115446 (2008)
CrossRef ADS Google scholar
[29]
A. V. Shytov , M. S. Rudner , and L. S. Levitov , Klein backscattering and Fabry–Pérot interference in graphene heterojunctions, Phys. Rev. Lett. 101 (15), 156804 (2008)
CrossRef ADS Google scholar
[30]
N. Stander , B. Huard , and D. Goldhaber-Gordon , Evidence for Klein tunneling in graphene p–n junctions, Phys. Rev. Lett. 102 (2), 026807 (2009)
CrossRef ADS Google scholar
[31]
A. F. Young and P. Kim , Quantum interference and Klein tunnelling in graphene heterojunctions, Nat. Phys. 5 (3), 222 (2009)
CrossRef ADS Google scholar
[32]
J. H. Bardarson , M. Titov , and P. Brouwer , Electrostatic confinement of electrons in an integrable graphene quantum dot, Phys. Rev. Lett. 102 (22), 226803 (2009)
CrossRef ADS Google scholar
[33]
H. Y. Chen , V. Apalkov , and T. Chakraborty , Fockdarwin states of Dirac electrons in graphene-based artificial atoms, Phys. Rev. Lett. 98 (18), 186803 (2007)
CrossRef ADS Google scholar
[34]
C. Downing , D. Stone , and M. Portnoi , Zero-energy states in graphene quantum dots and rings, Phys. Rev. B 84 (15), 155437 (2011)
CrossRef ADS Google scholar
[35]
A. Matulis and F. Peeters , Quasibound states of quantum dots in single and bilayer graphene, Phys. Rev. B 77 (11), 115423 (2008)
CrossRef ADS Google scholar
[36]
C. Schulz , R. Heinisch , and H. Fehske , Scattering of twodimensional Dirac fermions on gate-defined oscillating quantum dots, Phys. Rev. B 91 (4), 045130 (2015)
CrossRef ADS Google scholar
[37]
J. S. Wu and M. M. Fogler , Scattering of two-dimensional massless Dirac electrons by a circular potential barrier, Phys. Rev. B 90 (23), 235402 (2014)
CrossRef ADS Google scholar
[38]
H. Ji , Y. Pan , and H. Liu , Evolution of quasi-bound states in the circular n–p junction of bilayer graphene under magnetic field, Sci. Rep. 10 (1), 16256 (2020)
CrossRef ADS Google scholar
[39]
Y. Pan , H. Ji , X. Q. Li , and H. Liu , Quasi-bound states in an NPN-type nanometer-scale graphene quantum dot under a magnetic field, Sci. Rep. 10 (1), 20426 (2020)
CrossRef ADS Google scholar
[40]
J. Zhou , S. Cheng , W. You , and H. Jiang , Numerical study of Klein quantum dots in graphene systems, Sci. China Phys. Mech. Astron. 62 (6), 67811 (2019)
CrossRef ADS Google scholar
[41]
S. M. Reimann and M. Manninen , Electronic structure of quantum dots, Rev. Mod. Phys. 74 (4), 1283 (2002)
CrossRef ADS Google scholar
[42]
C. Gutiérrez , D. Walkup , F. Ghahari , C. Lewandowski , J. F. Rodriguez-Nieva , K. Watanabe , T. Taniguchi , L. S. Levitov , N. B. Zhitenev , and J. A. Stroscio , Interactiondriven quantum Hall wedding cake-like structures in graphene quantum dots, Science 361 (6404), 789 (2018)
CrossRef ADS Google scholar
[43]
J. F. Rodriguez-Nieva and L. S. Levitov , Berry phase jumps and giant nonreciprocity in Dirac quantum dots, Phys. Rev. B 94 (23), 235406 (2016)
CrossRef ADS Google scholar
[44]
P. McEuen , E. Foxman , J. Kinaret , U. Meirav , M. Kastner , N. S. Wingreen , and S. Wind , Self-consistent addition spectrum of a Coulomb island in the quantum Hall regime, Phys. Rev. B 45 (19), 11419 (1992)
CrossRef ADS Google scholar
[45]
D. Chklovskii , B. I. Shklovskii , and L. Glazman , Electrostatics of edge channels, Phys. Rev. B 46 (7), 4026 (1992)
CrossRef ADS Google scholar
[46]
M. Fogler , E. Levin , and B. Shklovskii , Chemical potential and magnetization of a Coulomb island, Phys. Rev. B 49 (19), 13767 (1994)
CrossRef ADS Google scholar
[47]
Y. V. Nazarov and A. Khaetskii , Wigner molecule on the top of a quantum dot, Phys. Rev. B 49 (7), 5077 (1994)
CrossRef ADS Google scholar
[48]
D. Chklovskii , K. Matveev , and B. I. Shklovskii , Ballistic conductance of interacting electrons in the quantum Hall regime, Phys. Rev. B 47 (19), 12605 (1993)
CrossRef ADS Google scholar
[49]
D. Xiao , M. C. Chang , and Q. Niu , Berry phase effects on electronic properties, Rev. Mod. Phys. 82 (3), 1959 (2010)
CrossRef ADS Google scholar
[50]
C. Dutreix , H. González-Herrero , I. Brihuega , M. Katsnelson , C. Chapelier , and V. Renard , Measuring the Berry phase of graphene from wavefront dislocations in Friedel oscillations, Nature 574 (7777), 219 (2019)
CrossRef ADS Google scholar
[51]
K. S. Novoselov , E. McCann , S. Morozov , V. I. Fal’ko , M. Katsnelson , U. Zeitler , D. Jiang , F. Schedin , and A. Geim , Unconventional quantum Hall effect and Berry’s phase of 2π in bilayer graphene, Nat. Phys. 2 (3), 177 (2006)
CrossRef ADS Google scholar
[52]
R. Resta , Macroscopic polarization in crystalline dielectrics: The geometric phase approach, Rev. Mod. Phys. 66 (3), 899 (1994)
CrossRef ADS Google scholar
[53]
G. M. Rutter , S. Jung , N. N. Klimov , D. B. Newell , N. B. Zhitenev , and J. A. Stroscio , Microscopic polarization in bilayer graphene, Nat. Phys. 7 (8), 649 (2011)
CrossRef ADS Google scholar
[54]
Y. Shimazaki , M. Yamamoto , I. V. Borzenets , K. Watanabe , T. Taniguchi , and S. Tarucha , Generation and detection of pure valley current by electrically induced Berry curvature in bilayer graphene, Nat. Phys. 11 (12), 1032 (2015)
CrossRef ADS Google scholar
[55]
A. Varlet , M. H. Liu , V. Krueckl , D. Bischoff , P. Simonet , K. Watanabe , T. Taniguchi , K. Richter , K. Ensslin , and T. Ihn , Fabry–Pérot interference in gapped bilayer graphene with broken anti-Klein tunneling, Phys. Rev. Lett. 113 (11), 116601 (2014)
CrossRef ADS Google scholar
[56]
Y. Zhang , Y. W. Tan , H. L. Stormer , and P. Kim , Experimental observation of the quantum Hall effect and Berry’s phase in graphene, Nature 438 (7065), 201 (2005)
CrossRef ADS Google scholar
[57]
K. S. Novoselov , A. K. Geim , S. V. Morozov , D. Jiang , M. I. Katsnelson , I. V. Grigorieva , S. V. Dubonos , and A. A. Firsov , Two-dimensional gas of massless Dirac fermions in graphene, Nature 438 (7065), 197 (2005)
CrossRef ADS Google scholar
[58]
D. L. Miller , K. D. Kubista , G. M. Rutter , M. Ruan , W. A. de Heer , P. N. First , and J. A. Stroscio , Observing the quantization of zero mass carriers in graphene, Science 324 (5929), 924 (2009)
CrossRef ADS Google scholar
[59]
Z. Q. Fu , Y. Zhang , J. B. Qiao , D. L. Ma , H. Liu , Z. H. Guo , Y. C. Wei , J. Y. Hu , Q. Xiao , X. R. Mao , and L. He , Spatial confinement, magnetic localization, and their interactions on massless Dirac fermions, Phys. Rev. B 98 (24), 241401 (2018)
CrossRef ADS Google scholar
[60]
A. Filinov , M. Bonitz , and Y. E. Lozovik , Wigner crystallization in mesoscopic 2D electron systems, Phys. Rev. Lett. 86 (17), 3851 (2001)
CrossRef ADS Google scholar
[61]
C. H. Zhang and Y. N. Joglekar , Wigner crystal and bubble phases in graphene in the quantum Hall regime, Phys. Rev. B 75 (24), 245414 (2007)
CrossRef ADS Google scholar
[62]
K. A. Guerrero-Becerra and M. Rontani , Wigner localization in a graphene quantum dot with a mass gap, Phys. Rev. B 90 (12), 125446 (2014)
CrossRef ADS Google scholar
[63]
H. González-Herrero , J. M. Gomez-Rodriguez , P. Mallet , M. Moaied , J. J. Palacios , C. Salgado , M. M. Ugeda , J. Y. Veuillen , F. Yndurain , and I. Brihuega , Atomic-scale control of graphene magnetism by using hydrogen atoms, Science 352 (6284), 437 (2016)
CrossRef ADS Google scholar
[64]
Y. Zhang , S. Y. Li , H. Huang , W. T. Li , J. B. Qiao , W. X. Wang , L. J. Yin , K. K. Bai , W. Duan , and L. He , Scanning tunneling microscopy of the π magnetism of a single carbon vacancy in graphene, Phys. Rev. Lett. 117 (16), 166801 (2016)
CrossRef ADS Google scholar
[65]
Y. Cao , V. Fatemi , A. Demir , S. Fang , S. L. Tomarken , J. Y. Luo , J. D. Sanchez-Yamagishi , K. Watanabe , T. Taniguchi , E. Kaxiras , R. C. Ashoori , and P. JarilloHerrero , Correlated insulator behaviour at half-filling in magic-angle graphene superlattices, Nature 556 (7699), 80 (2018)
CrossRef ADS Google scholar
[66]
Y. Cao , V. Fatemi , S. Fang , K. Watanabe , T. Taniguchi , E. Kaxiras , and P. Jarillo-Herrero , Unconventional superconductivity in magic-angle graphene superlattices, Nature 556 (7699), 43 (2018)
CrossRef ADS Google scholar
[67]
Y. W. Liu , J. B. Qiao , C. Yan , Y. Zhang , S. Y. Li , and L. He , Magnetism near half-filling of a van Hove singularity in twisted graphene bilayer, Phys. Rev. B 99, 201408(R) (2019)
CrossRef ADS Google scholar
[68]
G. Chen , A. L. Sharpe , P. Gallagher , I. T. Rosen , E. J. Fox , L. Jiang , B. Lyu , H. Li , K. Watanabe , T. Taniguchi , J. Jung , Z. Shi , D. Goldhaber-Gordon , Y. Zhang , and F. Wang , Signatures of tunable superconductivity in a trilayer graphene moiré superlattice, Nature 572 (7768), 215 (2019)
CrossRef ADS Google scholar
[69]
A. L. Sharpe , E. J. Fox , A. W. Barnard , J. Finney , K. Watanabe , T. Taniguchi , M. A. Kastner , and D. Goldhaber-Gordon , Emergent ferromagnetism near three-quarters filling in twisted bilayer graphene, Science 365 (6453), 605 (2019)
CrossRef ADS Google scholar
[70]
A. F. Young , C. R. Dean , L. Wang , H. Ren , P. CaddenZimansky , K. Watanabe , T. Taniguchi , J. Hone , K. L. Shepard , and P. Kim , Spin and valley quantum Hall ferromagnetism in graphene, Nat. Phys. 8 (7), 550 (2012)
CrossRef ADS Google scholar
[71]
S. Y. Li , Y. Zhang , L. J. Yin , and L. He , Scanning tunneling microscope study of quantum Hall isospin ferromagnetic states in the zero Landau level in a graphene monolayer, Phys. Rev. B 100 (8), 085437 (2019)
CrossRef ADS Google scholar
[72]
G. Chen , L. Jiang , S. Wu , B. Lyu , H. Li , B. L. Chittari , K. Watanabe , T. Taniguchi , Z. Shi , J. Jung , Y. Zhang , and F. Wang , Evidence of a gate-tunable Mott insulator in a trilayer graphene moiré superlattice, Nat. Phys. 15 (3), 237 (2019)
CrossRef ADS Google scholar
[73]
L. J. Yin , L. J. Shi , S. Y. Li , Y. Zhang , Z. H. Guo , and L. He , High-magnetic-field tunneling spectra of ABCstacked trilayer graphene on graphite, Phys. Rev. Lett. 122 (14), 146802 (2019)
CrossRef ADS Google scholar
[74]
G. Bester , D. Reuter , L. He , A. Zunger , P. Kailuweit , A. Wieck , U. Zeitler , J. Maan , O. Wibbelhoff , and A. Lorke , Experimental imaging and atomistic modeling of electron and hole quasiparticle wave functions in In As∕GaAs quantum dots, Phys. Rev. B 76 (7), 075338 (2007)
CrossRef ADS Google scholar
[75]
F. Cavaliere , U. D. Giovannini , M. Sassetti , and B. Kramer , Transport properties of quantum dots in the Wigner molecule regime, New J. Phys. 11 (12), 123004 (2009)
CrossRef ADS Google scholar
[76]
A. Ghosal , A. Güçlü , C. Umrigar , D. Ullmo , and H. U. Baranger , Correlation-induced inhomogeneity in circular quantum dots, Nat. Phys. 2 (5), 336 (2006)
CrossRef ADS Google scholar
[77]
A. Güçlü , P. Potasz , O. Voznyy , M. Korkusinski , and P. Hawrylak , Magnetism and correlations in fractionally filled degenerate shells of graphene quantum dots, Phys. Rev. Lett. 103 (24), 246805 (2009)
CrossRef ADS Google scholar
[78]
P. Potasz , A. Güçlü , and P. Hawrylak , Spin and electronic correlations in gated graphene quantum rings, Phys. Rev. B 82 (7), 075425 (2010)
CrossRef ADS Google scholar
[79]
M. Rontani and E. Molinari , Imaging quasiparticle wave functions in quantum dots via tunneling spectroscopy, Phys. Rev. B 71 (23), 233106 (2005)
CrossRef ADS Google scholar
[80]
B. Wunsch , T. Stauber , and F. Guinea , Electron-electron interactions and charging effects in graphene quantum dots, Phys. Rev. B 77 (3), 035316 (2008)
CrossRef ADS Google scholar
[81]
A. Güçlü , P. Potasz , and P. Hawrylak , Excitonic absorption in gate-controlled graphene quantum dots, Phys. Rev. B 82 (15), 155445 (2010)
CrossRef ADS Google scholar
[82]
Y. Li , H. Shu , S. Wang , and J. Wang , Electronic and optical properties of graphene quantum dots: The role of many-body effects, J. Phys. Chem. C 119 (9), 4983 (2015)
CrossRef ADS Google scholar
[83]
A. Franceschetti and A. Zunger , Direct pseudopotential calculation of exciton Coulomb and exchange energies in semiconductor quantum dots, Phys. Rev. Lett. 78 (5), 915 (1997)
CrossRef ADS Google scholar
[84]
A. Bostwick , F. Speck , T. Seyller , K. Horn , M. Polini , R. Asgari , A. H. MacDonald , and E. Rotenberg , Observation of plasmarons in quasi-freestanding doped graphene, Science 328 (5981), 999 (2010)
CrossRef ADS Google scholar
[85]
D. Elias , R. V. Gorbachev , A. Mayorov , S. Morozov , A. Zhukov , P. Blake , L. Ponomarenko , I. V. Grigorieva , K. S. Novoselov , F. Guinea , and A. K. Geim , Dirac cones reshaped by interaction effects in suspended graphene, Nat. Phys. 7 (9), 701 (2011)
CrossRef ADS Google scholar
[86]
J. P. Reed , B. Uchoa , Y. I. Joe , Y. Gan , D. Casa , E. Fradkin , and P. Abbamonte , The effective fine-structure constant of freestanding graphene measured in graphite, Science 330 (6005), 805 (2010)
CrossRef ADS Google scholar
[87]
D. A. Siegel , C. H. Park , C. Hwang , J. Deslippe , A. V. Fedorov , S. G. Louie , and A. Lanzara , Many-body interactions in quasi-freestanding graphene, Proc. Natl. Acad. Sci. USA 108 (28), 11365 (2011)
CrossRef ADS Google scholar
[88]
Y. Wang , V. W. Brar , A. V. Shytov , Q. Wu , W. Regan , H. Z. Tsai , A. Zettl , L. S. Levitov , and M. F. Crommie , Mapping Dirac quasiparticles near a single Coulomb impurity on graphene, Nat. Phys. 8 (9), 653 (2012)
CrossRef ADS Google scholar
[89]
R. H. Blick , D. Pfannkuche , R. Haug , K. Klitzing , and K. Eberl , Formation of a coherent mode in a double quantum dot, Phys. Rev. Lett. 80 (18), 4032 (1998)
CrossRef ADS Google scholar
[90]
D. Dixon , L. Kouwenhoven , P. McEuen , Y. Nagamune , J. Motohisa , and H. Sakaki , Influence of energy level alignment on tunneling between coupled quantum dots, Phys. Rev. B 53 (19), 12625 (1996)
CrossRef ADS Google scholar
[91]
A. W. Holleitner , R. H. Blick , A. K. Hüttel , K. Eberl , and J. P. Kotthaus , Probing and Controlling the Bonds of an Artificial Molecule, Science 297 (5578), 70 (2002)
CrossRef ADS Google scholar
[92]
T. Oosterkamp , T. Fujisawa , W. Van Der Wiel , K. Ishibashi , R. Hijman , S. Tarucha , and L. P. Kouwenhoven , Microwave spectroscopy of a quantum-dot molecule, Nature 395 (6705), 873 (1998)
CrossRef ADS Google scholar
[93]
B. Partoens and F. Peeters , Molecule-type phases and Hund’s rule in vertically coupled quantum dots, Phys. Rev. Lett. 84 (19), 4433 (2000)
CrossRef ADS Google scholar
[94]
G. Schedelbeck , W. Wegscheider , M. Bichler , and G. Abstreiter , Coupled quantum dots fabricated by cleaved edge overgrowth: From artificial atoms to molecules, Science 278 (5344), 1792 (1997)
CrossRef ADS Google scholar
[95]
F. Waugh , M. Berry , C. Crouch , C. Livermore , D. Mar , R. Westervelt , K. Campman , and A. Gossard , Measuring interactions between tunnel-coupled quantum dots, Phys. Rev. B 53 (3), 1413 (1996)
CrossRef ADS Google scholar
[96]
A. P. Alivisatos , Alivisatos, Semiconductor clusters, nanocrystals, and quantum dots, Science 271 (5251), 933 (1996)
CrossRef ADS Google scholar
[97]
R. E. Bailey and S. Nie , Alloyed semiconductor quantum dots: Tuning the optical properties without changing the particle size, J. Am. Chem. Soc. 125 (23), 7100 (2003)
CrossRef ADS Google scholar
[98]
L. Banszerus , B. Frohn , A. Epping , D. Neumaier , K. Watanabe , T. Taniguchi , and C. Stampfer , Gate-defined electron–hole double dots in bilayer graphene, Nano Lett. 18 (8), 4785 (2018)
CrossRef ADS Google scholar
[99]
M. Bayer , P. Hawrylak , K. Hinzer , S. Fafard , M. Korkusinski , Z. Wasilewski , O. Stern , and A. Forchel , Coupling and entangling of quantum states in quantum dot molecules, Science 291 (5503), 451 (2001)
CrossRef ADS Google scholar
[100]
I. L. Chuang , L. M. Vandersypen , X. Zhou , D. W. Leung , and S. Lloyd , Experimental realization of a quantum algorithm, Nature 393 (6681), 143 (1998)
CrossRef ADS Google scholar
[101]
N. Craig , J. Taylor , E. Lester , C. Marcus , M. Hanson , and A. Gossard , Tunable nonlocal spin control in a coupledquantum dot system, Science 304 (5670), 565 (2004)
CrossRef ADS Google scholar
[102]
M. Doty , M. Scheibner , I. Ponomarev , E. Stinaff , A. Bracker , V. Korenev , T. Reinecke , and D. Gammon , Electrically tunable g factors in quantum dot molecular spin states, Phys. Rev. Lett. 97 (19), 197202 (2006)
CrossRef ADS Google scholar
[103]
T. Fujisawa , T. H. Oosterkamp , W. G. Van der Wiel , B. W. Broer , R. Aguado , S. Tarucha , and L. P. Kouwenhoven , Spontaneous emission spectrum in double quantum dot devices, Science 282 (5390), 932 (1998)
CrossRef ADS Google scholar
[104]
C. R. Kagan and C. B. Murray , Charge transport in strongly coupled quantum dot solids, Nat. Nanotechnol. 10 (12), 1013 (2015)
CrossRef ADS Google scholar
[105]
J. Lobo-Checa , M. Matena , K. Müller , J. H. Dil , F. Meier , L. H. Gade , T. A. Jung , and M. Stöhr , Band formation from coupled quantum dots formed by a nanoporous network on a Copper surface, Science 325 (5938), 300 (2009)
CrossRef ADS Google scholar
[106]
Y. Pan , J. Yang , S. C. Erwin , K. Kanisawa , and S. Fölsch , Reconfigurable quantum-dot molecules created by atom manipulation, Phys. Rev. Lett. 115 (7), 076803 (2015)
CrossRef ADS Google scholar
[107]
L. Robledo , J. Elzerman , G. Jundt , M. Atatüre , A. Högele , S. Fält , and A. Imamoglu , Conditional dynamics of interacting quantum dots, Science 320 (5877), 772 (2008)
CrossRef ADS Google scholar
[108]
M. Scheibner , M. Yakes , A. S. Bracker , I. V. Ponomarev , M. Doty , C. Hellberg , L. Whitman , T. Reinecke , and D. Gammon , Optically mapping the electronic structure of coupled quantum dots, Nat. Phys. 4 (4), 291 (2008)
CrossRef ADS Google scholar
[109]
E. A. Stinaff , M. Scheibner , A. S. Bracker , I. V. Ponomarev , V. L. Korenev , M. E. Ware , M. F. Doty , T. L. Reinecke , and D. Gammon , Optical signatures of coupled quantum dots, Science 311 (5761), 636 (2006)
CrossRef ADS Google scholar
[110]
T. Unold , K. Mueller , C. Lienau , T. Elsaesser , and A. D. Wieck , Optical control of excitons in a pair of quantum dots coupled by the dipole–dipole interaction, Phys. Rev. Lett. 94 (13), 137404 (2005)
CrossRef ADS Google scholar
[111]
W. G. van der Wiel , S. De Franceschi , J. M. Elzerman , T. Fujisawa , S. Tarucha , and L. P. Kouwenhoven , Electron transport through double quantum dots, Rev. Mod. Phys. 75 (1), 1 (2002)
CrossRef ADS Google scholar
[112]
A. D. Yoffe , Semiconductor quantum dots and related systems: Electronic, optical, luminescence and related properties of low dimensional systems, Adv. Phys. 50 (1), 1 (2001)
CrossRef ADS Google scholar
[113]
Z. Q. Fu , Y. Pan , J. J. Zhou , K. K. Bai , D. L. Ma , Y. Zhang , J. B. Qiao , H. Jiang , H. Liu , and L. He , Relativistic artificial molecules realized by two coupled graphene quantum dots, Nano Lett. 20 (9), 6738 (2020)
CrossRef ADS Google scholar
[114]
J. B. Qiao , H. Jiang , H. Liu , H. Yang , N. Yang , K. Y. Qiao , and L. He , Bound states in nanoscale graphene quantum dots in a continuous graphene sheet, Phys. Rev. B 95 (8), 081409 (2017)
CrossRef ADS Google scholar
[115]
J. Güttinger , C. Stampfer , S. Hellmüller , F. Molitor , T. Ihn , and K. Ensslin , Charge detection in graphene quantum dots, Appl. Phys. Lett. 93 (21), 212102 (2008)
CrossRef ADS Google scholar
[116]
X. L. Liu , D. Hug , and L. M. Vandersypen , Gate-defined graphene double quantum dot and excited state spectroscopy, Nano Lett. 10 (5), 1623 (2010)
CrossRef ADS Google scholar
[117]
F. Molitor , S. Dröscher , J. Güttinger , A. Jacobsen , C. Stampfer , T. Ihn , and K. Ensslin , Transport through graphene double dots, Appl. Phys. Lett. 94 (22), 222107 (2009)
CrossRef ADS Google scholar
[118]
P. Silvestrov and K. Efetov , Quantum dots in graphene, Phys. Rev. Lett. 98 (1), 016802 (2007)
CrossRef ADS Google scholar
[119]
C. Stampfer , J. Güttinger , F. Molitor , D. Graf , T. Ihn , and K. Ensslin , Tunable Coulomb blockade in nanostructured graphene, Appl. Phys. Lett. 92 (1), 012102 (2008)
CrossRef ADS Google scholar
[120]
A. C. Bleszynski , F. A. Zwanenburg , R. Westervelt , A. L. Roest , E. P. Bakkers , and L. P. Kouwenhoven , Scanned probe imaging of quantum dots inside InAs nanowires, Nano Lett. 7 (9), 2559 (2007)
CrossRef ADS Google scholar
[121]
A. Deshpande , W. Bao , Z. Zhao , C. Lau , and B. J. LeRoy , Imaging charge density fluctuations in graphene using Coulomb blockade spectroscopy, Phys. Rev. B 83 (15), 155409 (2011)
CrossRef ADS Google scholar
[122]
P. Fallahi , A. C. Bleszynski , R. M. Westervelt , J. Huang , J. D. Walls , E. J. Heller , M. Hanson , and A. C. Gossard , Imaging a single-electron quantum dot, Nano Lett. 5 (2), 223 (2005)
CrossRef ADS Google scholar
[123]
K. A. Ritter and J. W. Lyding , The influence of edge structure on the electronic properties of graphene quantum dots and nanoribbons, Nat. Mater. 8 (3), 235 (2009)
CrossRef ADS Google scholar
[124]
X. Wang , Y. Ouyang , L. Jiao , H. Wang , L. Xie , J. Wu , J. Guo , and H. Dai , Graphene nanoribbons with smooth edges behave as quantum wires, Nat. Nanotechnol. 6 (9), 563 (2011)
CrossRef ADS Google scholar
[125]
M. T. Woodside and P. L. McEuen , Scanned probe imaging of single-electron charge states in nanotube quantum dots, Science 296 (5570), 1098 (2002)
CrossRef ADS Google scholar
[126]
D. Walkup , F. Ghahari , C. Gutiérrez , K. Watanabe , T. Taniguchi , N. B. Zhitenev , and J. A. Stroscio , Tuning single-electron charging and interactions between compressible Landau level islands in graphene, Phys. Rev. B 101 (3), 035428 (2020)
CrossRef ADS Google scholar
[127]
M. Amman , R. Wilkins , E. Ben-Jacob , P. Maker , and R. Jaklevic , Analytic solution for the current-voltage characteristic of two mesoscopic tunnel junctions coupled in series, Phys. Rev. B 43 (1), 1146 (1991)
CrossRef ADS Google scholar
[128]
A. Hanna , and M. Tinkham , Variation of the Coulomb staircase in a two-junction system by fractional electron charge, Phys. Rev. B 44 (11), 5919 (1991)
CrossRef ADS Google scholar
[129]
V. W. Brar , R. Decker , H. M. Solowan , Y. Wang , L. Maserati , K. T. Chan , H. Lee , Ç. O. Girit , A. Zettl , S. G. Louie , M. L. Cohen , and M. F. Crommie , Gate-controlled ionization and screening of cobalt adatoms on a graphene surface, Nat. Phys. 7 (1), 43 (2011)
CrossRef ADS Google scholar
[130]
D. Wong , L. Jr Velasco , J. Ju , S. Lee , H. Z. Kahn , C. Tsai , T. Germany , K. Taniguchi , A. Watanabe , F. Zettl , Wang , and M. F. Crommie , Characterization and manipulation of individual defects in insulating hexagonal boron nitride using scanning tunnelling microscopy, Nat. Nanotechnol. 10 (11), 949 (2015)
CrossRef ADS Google scholar
[131]
Y. J. Song , A. F. Otte , Y. Kuk , Y. Hu , D. B. Torrance , P. N. First , W. A. de Heer , H. Min , S. Adam , M. D. Stiles , A. H. MacDonald , and J. A. Stroscio , High-resolution tunnelling spectroscopy of a graphene quartet, Nature 467 (7312), 185 (2010)
CrossRef ADS Google scholar
[132]
L. J. Yin , S. Y. Li , J. B. Qiao , J. C. Nie , and L. He , Landau quantization in graphene monolayer, Bernal bilayer, and Bernal trilayer on graphite surface, Phys. Rev. B 91 (11), 115405 (2015)
CrossRef ADS Google scholar
[133]
S. Y. Li , H. Liu , J. B. Qiao , H. Jiang , and L. He , Magnetic-field-controlled negative differential conductance in scanning tunneling spectroscopy of graphene n–p–n junction resonators, Phys. Rev. B 97 (11), 115442 (2018)
CrossRef ADS Google scholar
[134]
S. Y. Li , K. K. Bai , W. J. Zuo , Y. W. Liu , Z. Q. Fu , W. X. Wang , Y. Zhang , L. J. Yin , J. B. Qiao , and L. He , Tunneling spectra of a quasifreestanding graphene monolayer, Phys. Rev. Appl. 9 (5), 054031 (2018)
CrossRef ADS Google scholar
[135]
T. Low and F. Guinea , Strain-induced pseudomagnetic field for novel graphene electronics, Nano Lett. 10 (9), 3551 (2010)
CrossRef ADS Google scholar
[136]
D. Abanin and D. Pesin , Interaction-induced topological insulator states in strained graphene, Phys. Rev. Lett. 109 (6), 066802 (2012)
CrossRef ADS Google scholar
[137]
B. Uchoa and Y. Barlas , Superconducting states in pseudo-Landau-levels of strained graphene, Phys. Rev. Lett. 111 (4), 046604 (2013)
CrossRef ADS Google scholar
[138]
B. Roy , Z. X. Hu , and K. Yang , Theory of unconventional quantum Hall effect in strained graphene, Phys. Rev. B 87 (12), 121408 (2013)
CrossRef ADS Google scholar
[139]
D. B. Zhang , G. Seifert , and K. Chang , Strain-induced pseudomagnetic fields in twisted graphene nanoribbons, Phys. Rev. Lett. 112 (9), 096805 (2014)
CrossRef ADS Google scholar
[140]
G. Wakker , R. P. Tiwari , and M. Blaauboer , Localization and circulating currents in curved graphene devices, Phys. Rev. B 84 (19), 195427 (2011)
CrossRef ADS Google scholar
[141]
B. Amorim , A. Cortijo , F. De Juan , A. Grushin , F. Guinea , A. Gutiérrez-Rubio , H. Ochoa , V. Parente , R. Roldán , P. San-Jose , J. Schiefele , M. Sturla , and M. A. H. Vozmediano , Novel effects of strains in graphene and other two dimensional materials, Phys. Rep. 617, 1 (2016)
CrossRef ADS Google scholar
[142]
M. Settnes , S. R. Power , and A. P. Jauho , Pseudomagnetic fields and triaxial strain in graphene, Phys. Rev. B 93 (3), 035456 (2016)
CrossRef ADS Google scholar
[143]
S. Y. Li , Y. Su , Y. N. Ren , and L. He , Valley polarization and inversion in strained graphene via pseudoLandau levels, valley splitting of real Landau levels, and confined states, Phys. Rev. Lett. 124, 106802 (2020)
CrossRef ADS Google scholar
[144]
E. McCann , Asymmetry gap in the electronic band structure of bilayer graphene, Phys. Rev. B 74 (16), 161403 (2006)
CrossRef ADS Google scholar
[145]
Y. Zhang , T. T. Tang , C. Girit , Z. Hao , M. C. Martin , A. Zettl , M. F. Crommie , Y. R. Shen , and F. Wang , Direct observation of a widely tunable bandgap in bilayer graphene, Nature 459 (7248), 820 (2009)
CrossRef ADS Google scholar
[146]
J. B. Oostinga , H. B. Heersche , X. Liu , A. F. Morpurgo , and L. M. Vandersypen , Gate-induced insulating state in bilayer graphene devices, Nat. Mater. 7 (2), 151 (2008)
CrossRef ADS Google scholar
[147]
L. J. Yin , H. Jiang , J. B. Qiao , and L. He , Direct imaging of topological edge states at a bilayer graphene domain wall, Nat. Commun. 7 (1), 11760 (2016)
CrossRef ADS Google scholar
[148]
L. Ju , Z. Shi , N. Nair , Y. Lv , C. Jin , C. Jr Velasco , H. A. Ojeda-Aristizabal , M. C. Bechtel , A. Martin , J. Zettl , Analytis , and F. Wang , Topological valley transport at bilayer graphene domain walls, Nature 520 (7549), 650 (2015)
CrossRef ADS Google scholar
[149]
L. J. Yin , Y. Zhang , J. B. Qiao , S. Y. Li , and L. He , Experimental observation of surface states and Landau levels bending in bilayer graphene, Phys. Rev. B 93 (12), 125422 (2016)
CrossRef ADS Google scholar
[150]
Y. T. Zhang , X. Xie , and Q. Sun , Effect of Zeeman splitting and interlayer bias potential on electron transport in bilayer graphene, Phys. Rev. B 86 (3), 035447 (2012)
CrossRef ADS Google scholar
[151]
J. Li , K. Wang , K. J. McFaul , Z. Zern , Y. Ren , K. Watanabe , T. Taniguchi , Z. Qiao , and J. Zhu , Gate-controlled topological conducting channels in bilayer graphene, Nat. Nanotechnol. 11 (12), 1060 (2016)
CrossRef ADS Google scholar
[152]
M. T. Allen , J. Martin , and A. Yacoby , Gate-defined quantum confinement in suspended bilayer graphene, Nat. Commun. 3 (1), 934 (2012)
CrossRef ADS Google scholar
[153]
A. M. Goossens , S. C. Driessen , T. A. Baart , K. Watanabe , T. Taniguchi , and L. M. Vandersypen , Gate-defined confinement in bilayer graphene–hexagonal boron nitride hybrid devices, Nano Lett. 12 (9), 4656 (2012)
CrossRef ADS Google scholar
[154]
J. Jr Velasco , D. Lee , S. Wong , H. Z. Kahn , J. Tsai , T. Costello , T. Umeda , K. Taniguchi , Watanabe , A. Zettl , F. Wang , and M. F. Crommie , Visualization and control of single-electron charging in bilayer graphene quantum dots, Nano Lett. 18 (8), 5104 (2018)
CrossRef ADS Google scholar
[155]
Y. Lee , A. Knothe , H. Overweg , M. Eich , C. Gold , A. Kurzmann , V. Klasovika , T. Taniguchi , K. Wantanabe , V. Fal’ko , T. Ihn , K. Ensslin , and P. Rickhaus , Tunable valley splitting due to topological orbital magnetic moment in bilayer graphene quantum point contacts, Phys. Rev. Lett. 124 (12), 126802 (2020)
CrossRef ADS Google scholar
[156]
M. Eich , F. Herman , R. Pisoni , H. Overweg , A. Kurzmann , Y. Lee , P. Rickhaus , K. Watanabe , T. Taniguchi , M. Sigrist , T. Ihn , and K. Ensslin , Spin and valley states in gate-defined bilayer graphene quantum dots, Phys. Rev. X 8 (3), 031023 (2018)
CrossRef ADS Google scholar
[157]
A. Kurzmann , M. Eich , H. Overweg , M. Mangold , F. Herman , P. Rickhaus , R. Pisoni , Y. Lee , R. Garreis , C. Tong , K. Watanabe , T. Taniguchi , K. Ensslin , and T. Ihn , Excited states in bilayer graphene quantum dots, Phys. Rev. Lett. 123 (2), 026803 (2019)
CrossRef ADS Google scholar
[158]
N. Gu , M. Rudner , and L. Levitov , Chirality-assisted electronic cloaking of confined states in bilayer graphene, Phys. Rev. Lett. 107 (15), 156603 (2011)
CrossRef ADS Google scholar
[159]
Z. Ge , F. Joucken , E. Quezada , D. R. Da Costa , J. Davenport , B. Giraldo , T. Taniguchi , K. Watanabe , N. P. Kobayashi , T. Low , and J. Jr Velasco , Visualization and manipulation of bilayer graphene quantum dots with broken rotational symmetry and nontrivial topology, Nano Lett. 20 (12), 8682 (2020)
CrossRef ADS Google scholar
[160]
C. H. Park and N. Marzari , Berry phase and pseudospin winding number in bilayer graphene, Phys. Rev. B 84 (20), 205440 (2011)
CrossRef ADS Google scholar
[161]
K. F. Mak , C. H. Lui , J. Shan , and T. F. Heinz , Observation of an electric-field-induced band gap in bilayer graphene by infrared spectroscopy, Phys. Rev. Lett. 102 (25), 256405 (2009)
CrossRef ADS Google scholar
[162]
T. Ohta , A. Bostwick , T. Seyller , K. Horn , and E. Rotenberg , Controlling the electronic structure of bilayer graphene, Science 313 (5789), 951 (2006)
CrossRef ADS Google scholar
[163]
Z. Hou , Y. F. Zhou , X. Xie , and Q. F. Sun , Berry phase induced valley level crossing in bilayer graphene quantum dots, Phys. Rev. B 99 (12), 125422 (2019)
CrossRef ADS Google scholar
[164]
R. Du , M. H. Liu , J. Mohrmann , F. Wu , R. Krupke , H. Von Löhneysen , K. Richter , and R. Danneau , Tuning anti-Klein to Klein tunneling in bilayer graphene, Phys. Rev. Lett. 121 (12), 127706 (2018)
CrossRef ADS Google scholar
[165]
W. Yao , D. Xiao , and Q. Niu , Valley-dependent optoelectronics from inversion symmetry breaking, Phys. Rev. B 77 (23), 235406 (2008)
CrossRef ADS Google scholar
[166]
R. Gorbachev , J. Song , G. Yu , A. Kretinin , F. Withers , Y. Cao , A. Mishchenko , I. Grigorieva , K. S. Novoselov , L. Levitov , and A. K. Geim , Detecting topological currents in graphene superlattices, Science 346 (6208), 448 (2014)
CrossRef ADS Google scholar
[167]
K. F. Mak , K. L. McGill , J. Park , and P. L. McEuen , The valley Hall effect in MoS2 transistors, Science 344 (6191), 1489 (2014)
CrossRef ADS Google scholar
[168]
S. Y. Xu , Q. Ma , H. Shen , V. Fatemi , S. Wu , T. R. Chang , G. Chang , A. M. M. Valdivia , C. K. Chan , Q. D. Gibson , J. Zhou , Z. Liu , K. Watanabe , T. Taniguchi , H. Lin , R. J. Cava , L. Fu , N. Gedik , and P. Jarillo-Herrero , Electrically switchable Berry curvature dipole in the monolayer topological insulator WTe2, Nat. Phys. 14 (9), 900 (2018)
CrossRef ADS Google scholar
[169]
H. Weng , C. Fang , Z. Fang , B. A. Bernevig , and X. Dai , Weyl semimetal phase in noncentrosymmetric transitionmetal monophosphides, Phys. Rev. X 5 (1), 011029 (2015)
CrossRef ADS Google scholar
[170]
S. Y. Xu , I. Belopolski , N. Alidoust , M. Neupane , G. Bian , C. Zhang , R. Sankar , G. Chang , Z. Yuan , C. C. Lee , S. M. Huang , H. Zheng , J. Ma , D. S. Sanchez , B. K. Wang , A. Bansil , F. Chou , P. P. Shibayev , H. Lin , S. Jia , and M. Z. Hasan , Discovery of a Weyl fermion semimetal and topological Fermi arcs, Science 349 (6248), 613 (2015)
CrossRef ADS Google scholar
[171]
B. Lv , H. Weng , B. Fu , X. P. Wang , H. Miao , J. Ma , P. Richard , X. Huang , L. Zhao , G. Chen , Z. Fang , X. Dai , T. Qian , and H. Ding , Experimental discovery of Weyl semimetal TaAs, Phys. Rev. X 5 (3), 031013 (2015)
CrossRef ADS Google scholar
[172]
M. Eich , R. Pisoni , A. Pally , H. Overweg , A. Kurzmann , Y. Lee , P. Rickhaus , K. Watanabe , T. Taniguchi , K. Ensslin , and T. Ihn , Coupled quantum dots in bilayer graphene, Nano Lett. 18 (8), 5042 (2018)
CrossRef ADS Google scholar
[173]
L. Banszerus , S. Möller , E. Icking , K. Watanabe , T. Taniguchi , C. Volk , and C. Stampfer , Single-electron double quantum dots in bilayer graphene, Nano Lett. 20 (3), 2005 (2020)
CrossRef ADS Google scholar
[174]
E. Clar and D. Stewart , Aromatic hydrocarbons. LXV. Triangulene derivatives, J. Am. Chem. Soc. 75 (11), 2667 (1953)
CrossRef ADS Google scholar
[175]
M. Melle-Franco , When 1 + 1 is odd, Nat. Nanotechnol. 12 (4), 292 (2017)
CrossRef ADS Google scholar
[176]
Y. Morita , S. Suzuki , K. Sato , and T. Takui , Synthetic organic spin chemistry for structurally well-defined openshell graphene fragments, Nat. Chem. 3 (3), 197 (2011)
CrossRef ADS Google scholar
[177]
E. H. Lieb , Two theorems on the Hubbard model, Phys. Rev. Lett. 62 (10), 1201 (1989)
CrossRef ADS Google scholar
[178]
P. Potasz , A. Güçlü , and P. Hawrylak , Zero-energy states in triangular and trapezoidal graphene structures, Phys. Rev. B 81 (3), 033403 (2010)
CrossRef ADS Google scholar
[179]
J. Fernández-Rossier and J. J. Palacios , Magnetism in graphene nanoislands, Phys. Rev. Lett. 99 (17), 177204 (2007)
CrossRef ADS Google scholar
[180]
W. L. Wang , S. Meng , and E. Kaxiras , Graphene nanoflakes with large spin, Nano Lett. 8 (1), 241 (2008)
CrossRef ADS Google scholar
[181]
A. Heinrich , J. Gupta , C. Lutz , and D. Eigler , Singleatom spin-flip spectroscopy, Science 306 (5695), 466 (2004)
CrossRef ADS Google scholar
[182]
C. F. Hirjibehedin , C. P. Lutz , and A. J. Heinrich , Spin coupling in engineered atomic structures, Science 312 (5776), 1021 (2006)
CrossRef ADS Google scholar
[183]
S. Baumann , W. Paul , T. Choi , C. P. Lutz , A. Ardavan , and A. J. Heinrich , Electron paramagnetic resonance of individual atoms on a surface, Science 350 (6259), 417 (2015)
CrossRef ADS Google scholar
[184]
W. L. Wang , O. V. Yazyev , S. Meng , and E. Kaxiras , Topological frustration in graphene nanoflakes: Magnetic order and spin logic devices, Phys. Rev. Lett. 102 (15), 157201 (2009)
CrossRef ADS Google scholar
[185]
W. Han , R. K. Kawakami , M. Gmitra , and J. Fabian , Graphene spintronics, Nat. Nanotechnol. 9 (10), 794 (2014)
CrossRef ADS Google scholar
[186]
N. Pavliček , A. Mistry , Z. Majzik , N. Moll , G. Meyer , D. J. Fox , and L. Gross , Synthesis and characterization of triangulene, Nat. Nanotechnol. 12 (4), 308 (2017)
CrossRef ADS Google scholar
[187]
G. Allinson , R. J. Bushby , J. L. Paillaud , D. Oduwole , and K. Sales , ESR spectrum of a stable triplet π biradical: Trioxytriangulene, J. Am. Chem. Soc. 115 (5), 2062 (1993)
CrossRef ADS Google scholar
[188]
J. Inoue , K. Fukui , T. Kubo , S. Nakazawa , K. Sato , D. Shiomi , Y. Morita , K. Yamamoto , T. Takui , and K. Nakasuji , The first detection of a Clar’s hydrocarbon, 2,6,10-tri-tert-butyltriangulene: A ground-state triplet of non-Kekulé polynuclear benzenoid hydrocarbon, J. Am. Chem. Soc. 123 (50), 12702 (2001)
CrossRef ADS Google scholar
[189]
G. Allinson , R. J. Bushby , M. V. Jesudason , J.-L. Paillaud , and N. Taylor , The synthesis of singlet ground state derivatives of non-Kekulé polynuclear aromatics, J. Chem. Soc. Perkin Trans, 2, 147 (1997)
CrossRef ADS Google scholar
[190]
N. Pavliček , I. Swart , J. Niedenführ , G. Meyer , and J. Repp , Symmetry dependence of vibration-assisted tunneling, Phys. Rev. Lett. 110 (13), 136101 (2013)
CrossRef ADS Google scholar
[191]
J. Repp , G. Meyer , S. Paavilainen , F. E. Olsson , and M. Persson , Imaging bond formation between a gold atom and pentacene on an insulating surface, Science 312 (5777), 1196 (2006)
CrossRef ADS Google scholar
[192]
P. Jia , W. Chen , J. Qiao , M. Zhang , X. Zheng , Z. Xue , R. Liang , C. Tian , L. He , Z. Di , and X. Wang , Programmable graphene nanobubbles with three-fold symmetric pseudo-magnetic fields, Nat. Commun. 10 (1), 3127 (2019)
CrossRef ADS Google scholar
[193]
Y. W. Liu , Y. Su , X. F. Zhou , L. J. Yin , C. Yan , S. Y. Li , W. Yan , S. Han , Z. Q. Fu , Y. Zhang , Q. Yang , Y. N. Ren , and L. He , Tunable lattice reconstruction, triangular network of chiral one-dimensional states, and bandwidth of flat bands in magic angle twisted bilayer graphene, Phys. Rev. Lett. 125 (23), 236102 (2020)
CrossRef ADS Google scholar
[194]
S. Y. Li , Y. Zhang , Y. N. Ren , J. Liu , X. Dai , and L. He , Experimental evidence for orbital magnetic moments generated by moiré-scale current loops in twisted bilayer graphene, Phys. Rev. B 102 (12), 121406 (2020)
CrossRef ADS Google scholar
[195]
J. Cai , P. Ruffeux , R. Jaafar , M. Bieri , T. Braun , S. Blankenburg , M. Muoth , A. P. Seitsonen , M. Saleh , X. Feng , K. Müllen , and R. Fasel , Atomically precise bottom-up fabrication of graphene nanoribbons, Nature 466 (7305), 470 (2010)
CrossRef ADS Google scholar
[196]
P. Ruffeux , S. Wang , B. Yang , C. Sánchez-Sánchez , J. Liu , T. Dienel , L. Talirz , P. Shinde , C. A. Pignedoli , D. Passerone , T. Dumslaff , X. Feng , K. Müllen , and R. Fasel , On-surface synthesis of graphene nanoribbons with zigzag edge topology, Nature 531 (7595), 489 (2016)
CrossRef ADS Google scholar
[197]
M. Di Giovannantonio , O. Deniz , J. I. Urgel , R. Widmer , T. Dienel , S. Stolz , C. Sánchez-Sánchez , M. Muntwiler , T. Dumslaff , R. Berger , A. Narita , X. Feng , K. Müllen , P. Ruffeux , and R. Fasel , On-surface growth dynamics of graphene nanoribbons: The role of halogen functionalization, ACS Nano 12 (1), 74 (2018)
CrossRef ADS Google scholar
[198]
Y. C. Chen , T. Cao , C. Chen , Z. Pedramrazi , D. Haberer , D. G. De Oteyza , F. R. Fischer , S. G. Louie , and M. F. Crommie , Molecular bandgap engineering of bottom-up synthesized graphene nanoribbon heterojunctions, Nat. Nanotechnol. 10 (2), 156 (2015)
CrossRef ADS Google scholar
[199]
M. Treier , C. A. Pignedoli , T. Laino , R. Rieger , K. Müllen , D. Passerone , and R. Fasel , Surface-assisted cyclodehydrogenation provides a synthetic route towards easily processable and chemically tailored nanographenes, Nat. Chem. 3 (1), 61 (2011)
CrossRef ADS Google scholar
[200]
J. Cai , C. A. Pignedoli , L. Talirz , P. Ruffeux , H. Söde , L. Liang , V. Meunier , R. Berger , R. Li , X. Feng , K. Müllen , and R. Fasel , Graphene nanoribbon heterojunctions, Nat. Nanotechnol. 9 (11), 896 (2014)
CrossRef ADS Google scholar
[201]
O. Gröning , S. Wang , X. Yao , C. A. Pignedoli , G. Borin Barin , C. Daniels , A. Cupo , V. Meunier , X. Feng , A. Narita , K. Müllen , P. Ruffeux , and R. Fasel , Engineering of robust topological quantum phases in graphene nanoribbons, Nature 560 (7717), 209 (2018)
CrossRef ADS Google scholar
[202]
S. Wang , N. Kharche , E. Costa Girão , X. Feng , K. Müllen , V. Meunier , R. Fasel , and P. Ruffeux , Quantum dots in graphene nanoribbons, Nano Lett. 17 (7), 4277 (2017)
CrossRef ADS Google scholar
[203]
F. J. Giessibl , Advances in atomic force microscopy, Rev. Mod. Phys. 75 (3), 949 (2003)
CrossRef ADS Google scholar
[204]
F. Mohn , B. Schuler , L. Gross , and G. Meyer , Different tips for high-resolution atomic force microscopy and scanning tunneling microscopy of single molecules, Appl. Phys. Lett. 102 (7), 073109 (2013)
CrossRef ADS Google scholar
[205]
L. Gross , F. Mohn , N. Moll , P. Liljeroth , and G. Meyer , The chemical structure of a molecule resolved by atomic force microscopy, Science 325 (5944), 1110 (2009)
CrossRef ADS Google scholar
[206]
F. J. Giessibl , High-speed force sensor for force microscopy and profilometry utilizing a quartz tuning fork, Appl. Phys. Lett. 73 (26), 3956 (1998)
CrossRef ADS Google scholar
[207]
D. J. Choi , N. Lorente , J. Wiebe , K. Von Bergmann , A. F. Otte , and A. J. Heinrich , Atomic spin chains on surfaces, Rev. Mod. Phys. 91 (4), 041001 (2019)
CrossRef ADS Google scholar
[208]
G. Trinquier , N. Suaud , N. Guihéry , and J. P. Malrieu , Designing magnetic organic lattices from high-spin polycyclic units, ChemPhysChem 12 (16), 3020 (2011)
CrossRef ADS Google scholar
[209]
X. Li , J. Zhou , Q. Wang , X. Chen , Y. Kawazoe , and P. Jena , Magnetism of two-dimensional triangular nanoflake-based kagome lattices, New J. Phys. 14 (3), 033043 (2012)
CrossRef ADS Google scholar
[210]
X. Li and Q. Wang , Tunable ferromagnetism in assembled two dimensional triangular graphene nanoflakes, Phys. Chem. Chem. Phys. 14 (6), 2065 (2012)
CrossRef ADS Google scholar
[211]
S. Khanna and J. Lambe , Inelastic electron tunneling spectroscopy, Science 220 (4604), 1345 (1983)
CrossRef ADS Google scholar
[212]
Y. Zhang , V. W. Brar , F. Wang , C. Girit , Y. Yayon , M. Panlasigui , A. Zettl , and M. F. Crommie , Giant phononinduced conductance in scanning tunnelling spectroscopy of gate-tunable graphene, Nat. Phys. 4 (8), 627 (2008)
CrossRef ADS Google scholar
[213]
M. Ternes , Spin excitations and correlations in scanning tunneling spectroscopy, New J. Phys. 17 (6), 063016 (2015)
CrossRef ADS Google scholar
[214]
S. Mishra , D. Beyer , K. Eimre , S. Kezilebieke , R. Berger , O. Gröning , C. A. Pignedoli , K. Müllen , P. Liljeroth , P. Ruffeux , X. Feng , and R. Fasel , Topological frustration induces unconventional magnetism in a nanographene, Nat. Nanotechnol. 15 (1), 22 (2020)
CrossRef ADS Google scholar
[215]
J. Su , W. Fan , P. Mutombo , X. Peng , S. Song , M. Ondráček , P. Golub , J. Brabec , L. Veis , M. Telychko , P. Jelínek , J. Wu , and J. Lu , On-surface synthesis and characterization of [7]triangulene quantum ring, Nano Lett. 21 (1), 861 (2021)
CrossRef ADS Google scholar
[216]
J. Li , S. Sanz , M. Corso , D. J. Choi , D. Peña , T. Frederiksen , and J. I. Pascual , Single spin localization and manipulation in graphene open-shell nanostructures, Nat. Commun. 10, 200 (2019)
CrossRef ADS Google scholar

RIGHTS & PERMISSIONS

2022 The Author(s) 2022. This article is published with open access at link.springer.com and journal.hep.com.cn
AI Summary AI Mindmap
PDF(4585 KB)

Accesses

Citations

Detail

Sections
Recommended

/